Problem 19 worked answer

Pen Nib’s First Move

Designed for Grade 3 · Uses Early Grade 3 math · About 2–6 minutes

Earn one jewelTumbled GarnetLevel 2

At a glance

  • Part 1: Strike first, then Cleave, deals 20 damage.
  • Part 2: Cleave first, then Strike, deals 22 damage, which is 2 more.

1. Strike first

Pen Nib doubles Strike’s 6 damage:

Cleave then deals its normal 8 damage:

The Ironclad deals 20 total damage.

2. Change only the order

If Cleave is first, Pen Nib doubles its 8 damage:

Strike then deals its normal 6 damage:

So Cleave first, then Strike, is the better order. It deals 22 total damage.

Why the order matters

The two plans both include one normal 6 and one normal 8. Pen Nib adds one extra copy of the first Attack’s damage:

  • Strike first adds an extra 6.
  • Cleave first adds an extra 8.

The ordinary sum stays the same, but the extra copy is larger when Cleave goes first. That makes the better total exactly damage greater.

Check

, so the two totals differ by the same amount as the two normal Attack values.

Technical fit and rating

MJ 3.0 · C2 · W1 Standard challenge · Light workload

Number and operations

How the rating works →

mathjewels.com/answers/problems/19/

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